摘要
讨论极小曲面方程的求解 .极小曲面方程是一个高度非线性的二阶椭圆偏微分方程 ,求解十分困难 .该文基于有限元方法 ,使用一个简单而有效的线性化策略 ,将问题转化为一系列线性问题 ,从而大大简化了求解过程 .数值结果表明该方法简单有效 。
In this paper the numerical solution of the minimal surface equation is investigated. The method is based on the finite element method (FEM). The minimal surface equation is strongly nonlinear. While we apply the FEM and Newton iteration method solving it, the global stiff matrix is varies as the iterations are proceeding and each of the iterations involves many complicated time consuming derivative calculations. In addition, the selection of the initial guess is very important to resolve the nonlinear problem. We appeal to a global method called numerical extension method in the whole iterative process and linearize the nonlinear finite element system using a simple iteration.
出处
《计算机学报》
EI
CSCD
北大核心
2003年第4期507-510,共4页
Chinese Journal of Computers
基金
国家"九七三"重点基础研究发展规划项目 (G19980 30 6 0 0 )
国家自然科学基金 ( 6 99730 4 2 )资助
